In a Couette flow, two large flat plates lie one on top of another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity V in the top plate relative to the bottom plate is given by V = τh/μ, where τ is the shear stress applied to the top plate, h is the thickness of the fluid layer, and μ is the viscosity of the fluid. Assume that μ = 1.49 Pa • s and h = 10 mm, both with negligible uncertainty.

a. Suppose that τ = 30.0 ± 0.1 Pa. Estimate V, and find the uncertainty in the estimate.

b. If it is desired to estimate V with an uncertainty of 0.2 mm/s, what must be the uncertainty in τ?

Answer :

Step 1 of 3:

Given the velocity V in the top plate relative to the bottom plate is given by

Where, is the shear stress applied to the top plate.

h is the thickness of the fluid layer.

is the viscosity of the fluid.

Given that, and h = 10 mm.